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Algebraic Methods for Stronger Crypto

Objective

Our field is cryptology. Our overarching objective is to advance significantly the frontiers in
design and analysis of high-security cryptography for the future generation.
Particularly, we wish to enhance the efficiency, functionality, and, last-but-not-least, fundamental understanding of cryptographic security against very powerful adversaries.
Our approach here is to develop completely novel methods by
deepening, strengthening and broadening the
algebraic foundations of the field.
Concretely, our lens builds on
the arithmetic codex. This is a general, abstract cryptographic primitive whose basic theory we recently developed and whose asymptotic part, which relies on algebraic geometry, enjoys crucial applications in surprising foundational results on constant communication-rate two-party cryptography. A codex is a linear (error correcting) code that, when endowing its ambient vector space just with coordinate-wise multiplication, can be viewed as simulating, up to some degree, richer arithmetical structures such as finite fields (or products thereof), or generally, finite-dimensional algebras over finite fields. Besides this degree, coordinate-localities for which simulation holds and for which it does not at all are also captured.
Our method is based on novel perspectives on codices which significantly
widen their scope and strengthen their utility. Particularly, we bring
symmetries, computational- and complexity theoretic aspects, and connections with algebraic number theory, -geometry, and -combinatorics into play in novel ways. Our applications range from public-key cryptography to secure multi-party computation.
Our proposal is subdivided into 3 interconnected modules:


(1) Algebraic- and Number Theoretical Cryptanalysis
(2) Construction of Algebraic Crypto Primitives
(3) Advanced Theory of Arithmetic Codices

Call for proposal

ERC-2016-ADG
See other projects for this call

Host institution

STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN
Address
Winthontlaan 2
3526 KV Utrecht
Netherlands
Activity type
Research Organisations
EU contribution
€ 2 447 439

Beneficiaries (1)

STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN
Netherlands
EU contribution
€ 2 447 439
Address
Winthontlaan 2
3526 KV Utrecht
Activity type
Research Organisations